1. Field of Invention
The present invention relates to signal processing in Nuclear Magnetic Resonance (NMR) and other spectroscopic techniques.
2. Background
In NMR spectroscopy, as well as in other spectroscopic methods, noise reduction can be a serious problem. In most experimental NMR studies, excessive noise can be present in the measured time domain signal, which decays exponentially and is thus called an FID (“free induction decay”) signal. Because of the noise, the Fourier transformed spectrum may not allow the underlying spectrum to be reliably differentiated or extracted from the noise.
A number of methods are known in the art for reducing noise in NMR studies. Signal averaging over many transients or scans is widely known. In signal averaging, however, the signal grows relatively slowly over time. Also, other factors such as sample concentration, magnetic field strength, and NMR machine design frequently affect the intensity of the NMR signal, which is inherently rather weak. Because of these factors, the needed number of transients may often be very high. When the fast Fourier transform method is used to derive the spectrum from the measured data, the requisite number of transients may be too high for certain experiments to be practically feasible.
Many attempts have been made to address this problem by developing data processing methods that can extract signal information from noisy data using available knowledge regarding the model for the underlying signal. One known method is harmonic inversion, which is a parameter fitting model that extracts the desired spectral parameters by fitting the data to a sum of damped harmonics. The knowledge used here is that a linear combination of complex decaying exponentials can be assumed to be a good model for an NMR FID signal. The equations that relate the measured FID signal to such a model directly yield, when solved, spectral parameters such as the position, width, and intensity of each nuclear resonance, so that a spectrum can be reconstructed from these parameters.
The harmonic inversion method achieves a higher spectral resolution, for a given signal length, compared to the Fourier transform method. The solutions to the harmonic inversion equations, however, can be extremely sensitive to small noise perturbations. Various regularization techniques have been proposed. With no noise or with very little noise, the harmonic inversion method usually provides acceptable results when used with these regularization schemes. At typical noise levels, however, the harmonic inversion method together with the regularization schemes may yield inconsistent and unreliable results, producing spectra with false or missing spectral lines.
For these reasons, there is a need for a method and system that allows reliable spectra to be derived from spectroscopic data, without requiring an excessive number of transient acquisitions.